New Solids:CYLINDERS, PYRAMIDS,CONES, SPHERES

Challenge Questions

Projects and exam area next week!

Sites: 1, 2, 3, mathsnacks.orgVideos (Bubbles is #2): 1, 2

Agenda for today

Have 2 identicalfaces (bases)

The two bases are circles

The two bases lie in parallel planes

Solids: Cylinders

Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases

SIXTHPROBLEMSET (from last time)

Solids: Cylinders (cont'd)

Recall the formula for SA of a prism

Compare it to our cylinder formula

Solids: Cylinders (cont'd)

Recall the formula for V of a prism

Compare it to our cylinder formula

Solids: Cylinders (cont'd)

Label a cylinder’s height and radius

Find the surface area of a prism

Find the volume of a prism

SEVENTH PROBLEM SET

Cylinders TASKS

Discussion question:Which cylinder makes

a better container?

Solids: Cylinders (cont'd)

Solids: Pyramids

Have a polygon for a base

Have triangles that join the base to the apex

Have some tricky terminology…

Pyramids (continued)

Height (also known as altitude) is the perpendicular distance between base and apex

Pyramids (continued)

Slant height is the distance between the apex and the center of the base’s edge

FIRST PROBLEM SET

Here is the surface area formula:

P is perimeter of the baseS is slant heightBA is area of the base

Pyramids (continued)

Here is the volume formula:

BA is area of the baseH is height (or altitude)

Pyramids (continued)

Correctly label a pyramid’s apex, base, height, and slant height

Find the surface area of a square pyramid

Find the volume of a square pyramid

SECOND PROBLEM SET

Pyramids TASKS

Solids: Cones

Have a circle for a base

Have an apex

Have both height and slant height

Cones (continued)

“In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Here’s the formula for surface area:

“r” is radius of the base“S” is slant height

Cones (continued)

Here’s the formula for volume:

“H” is height (or altitude)

Cones (continued)

Correctly label a cone’s apex, base, height, and slant height

Find the surface area of a right cone

Find the volume of a cone

THIRD PROBLEM SET

Cones TASKS

Solids: Spheres

Have a radius

Have the otherCircle stuff

Spheres (continued)

Come up with the formula for SA…

Here is the surface area formula:

(This formula wierds me out: why is it so simple?)

Spheres (continued)

Here is the volume formula:

(notice that r is cubed)

FOURTH PROBLEM SET

Spheres (continued)

Find the surface area of a sphere

Find the volume of a sphere

Work with combinations

FIFTH PROBLEM SET

Spheres TASKS

Why do elephants have big ears?

Seven Bridges of Konigsberg Link

Predict the Mobius strip’s split Link

Challenge Questions